In unstructured P2P networks, the existing search protocols are effective for popular resources, but searching for scarce resources is inefficient. Improving copy rates of scarce resources is the main method to solve the search inefficiency. The query hit rates on scarce resources are lower as copies of scarce resources are small. So the existing passive copy replication strategies based on the success queries are not suitable for the improvement of rare resources popularity. To solve this problem, we propose an active replication and search strategy of scarce resources. In the search process, peers with scarce resources actively initiate the search for scarce resources. And local demand information is effectively obtained in the process of search, and then scarce resources are copied to the peers that have demands for the scarce resources. The method implements the on-demand replication of scarce resources to improve popularity and query hit rates of scarce resources. Based on local requirement information, we provide three different kinds of on-demand replication strategies and a rare resource search algorithm. Experimental results show that the active replication and search strategy of scarce resources can effectively increase copy rates of scarce resources with lower replication consumption and network overhead, and then improve the query hit rates of scarce resources.